We have calculated for all the models presented in AH the total radiative losses, , given by
where L is the local net radiative loss function as calculated by AH and is the position of the outer boundary with . The total heating from inflow amounts to
because one has inflow from both sides of the prominence. We take K and is either 6500 K or 8000 K, depending on the model. For the inflow we take cm-2 s-1, which corresponds to a coronal density of cm-3 and a flow velocity in the corona of cm s-1 at K. This then scales to cm -3 and cm s-1 at T = 30000 K. Our value for the coronal inflow velocity is rather large (i.e. 1/2 of the local sound velocity), therefore the resulting estimates for the heating can be considered as upper limits. The value of the ratio amounts to about 0.8 for the thick slab models of AH and 0.3 for the thin slabs. The relevant quantities for all our models are summarized in Table 1. The models are denoted in the same way as in AH: M1 to M3 refers to geometrically thick slabs, M4 to M6 to geometrically thin slabs; T6 stands for = 6500 K and T8 for = 8000 K. M is the total column mass in g cm-2, D the slab thickness in km, the integrated radiative losses, the heating by inflow, both in erg cm-2s-1, and the radiative losses per unit mass, in erg g-1s-1.
From our table we see that only the low mass models M3T6, M6T6 and M6T8 are in energy equilibrium. The models M3T8 and M5T6 are close to an equilibrium. All other models cannot be balanced by the inflow of enthalpy and ionisation energy and will therefore require some additional heating mechanism. This implies that an energy equilibrium by an inflow mechanism can be achieved only for sufficiently cool and very tenuous prominences.
We have also calculated the ratio between total radiative losses and column mass. These ratios as calculated in Table 1 are shown in Fig. 1 as a function of column mass for two different values of the central temperature. The two curves to the left are for thin slabs, the ones to the right for thick slabs. The ratio changes by a factor of 10 for the range of column masses taken in our models. The fact that the most massive prominences also have the largest specific losses can be explained by realising that the optically thin contributions to the radiative losses are proportional to the square of the particle density. Table 1 and Fig. 1 also show that models which have the same mean gas pressure, but different column masses (e.g. models M1 and M4, etc.) have approximately the same value for the ratio .
© European Southern Observatory (ESO) 2000
Online publication: June 20, 2000